Answered: A particular fruit's weights are…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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1.A particular fruit's weights are normally distributed, with a mean of 488 grams and a standard deviation of 11 grams.

If you pick one fruit at random, what is the probability that it will weigh between 464 grams and 472 grams_______________

2. A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 210.2-cm and a standard deviation of 1.1-cm.

A steel rod is chosen at random from all those produced by the company. What is the probability that the length of this rod is greater than 206.8 cm.

_____________________
Enter your answer as a number accurate to 4 decimal places.

3. A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 99.5-cm and a standard deviation of 0.5-cm.

Find the proportion of steel rods with lengths between 100.2 cm and 101.1 cm.
________________

Enter your answer as a number accurate to 4 decimal places.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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